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Improved Bound for Dilation of an Embedding onto Circulant Networks

  • R. Sundara Rajan
  • T. M. Rajalaxmi
  • Joe Ryan
  • Mirka Miller
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Implementation of parallel algorithms and simulation of different interconnection networks need an effective tool, that is, graph embedding. This paper focuses on improving a lower bound obtained in Rajan et al. (Comput J 58:3271–3278, 2015) for dilation of an embedding onto circulant networks. In addition, this paper provides algorithms to compute dilation of embedding circulant network into certain trees, for instance, m-rooted complete binary tree, m-rooted sibling tree, and r-dimensional hypertree, proving that the improved bound obtained is sharp.

Keywords

Embedding Dilation Circulant network Binary tree Sibling tree Hypertree 

Mathematics Subject Classification

05C60 05C85 

Notes

Acknowledgement

The work of R. Sundara Rajan was partially supported by Project No. ECR/2016/1993, Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • R. Sundara Rajan
    • 1
  • T. M. Rajalaxmi
    • 2
  • Joe Ryan
    • 3
  • Mirka Miller
    • 4
  1. 1.Department of MathematicsHindustan Institute of Technology and SciencePadur, ChennaiIndia
  2. 2.Department of MathematicsSSN College of EngineeringKalavakkam, ChennaiIndia
  3. 3.School of Electrical Engineering and Computer ScienceThe University of NewcastleCallaghanAustralia
  4. 4.School of Mathematical and Physical SciencesThe University of NewcastleCallaghanAustralia

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